Solve frac{sqrt{24*26(24+26+10)(24+26-10)}}{24+26}

$$\frac{ \sqrt{ 24 \times 26(24+26+10)(24+26-10) } }{ 24+26 }$$

Evaluate

$$\frac{24\sqrt{26}}{5}\approx 24.475293665$$

Solution Steps

Multiply 24 and 26 to get 624.

$$\frac{\sqrt{624\left(24+26+10\right)\left(24+26-10\right)}}{24+26}$$

Add 24 and 26 to get 50.

$$\frac{\sqrt{624\left(50+10\right)\left(24+26-10\right)}}{24+26}$$

Add 50 and 10 to get 60.

$$\frac{\sqrt{624\times 60\left(24+26-10\right)}}{24+26}$$

Multiply 624 and 60 to get 37440.

$$\frac{\sqrt{37440\left(24+26-10\right)}}{24+26}$$

Add 24 and 26 to get 50.

$$\frac{\sqrt{37440\left(50-10\right)}}{24+26}$$

Subtract 10 from 50 to get 40.

$$\frac{\sqrt{37440\times 40}}{24+26}$$

Multiply 37440 and 40 to get 1497600.

$$\frac{\sqrt{1497600}}{24+26}$$

Factor 1497600=240^{2}\times 26. Rewrite the square root of the product \sqrt{240^{2}\times 26} as the product of square roots \sqrt{240^{2}}\sqrt{26}. Take the square root of 240^{2}.

$$\frac{240\sqrt{26}}{24+26}$$

Add 24 and 26 to get 50.

$$\frac{240\sqrt{26}}{50}$$

Divide 240\sqrt{26} by 50 to get \frac{24}{5}\sqrt{26}.

$$\frac{24}{5}\sqrt{26}$$